Question

A radioactive isotope having a half life of $3\text{days}$ was received after $9\text{days}$. It was found that there was only $4\text{gm}$ of the isotope in the container. The initial weight of the isotope when packed was

• A. $8\text{g}$
• B. $16\text{g}$
• C. $24\text{g}$
• D. $32\text{g}$

Answer 1

The correct option is D $32\text{g}$

Given:
$t=9\text{days};T_{1/2}=3\text{days}$

Number of half days,

$n=\frac{t}{T_{1/2}}=\frac{9}{3}=3$

Now, using $\frac{W}{W_0}=\frac{1}{2^n}$

$\Rightarrow \frac{4}{W_0}=\frac{1}{2^3}$

$\therefore W_0=2^3\times 4=32\text{g}$

Hence, $\left(\text{D}\right)$ is the correct answer.